The wooden clarinet, as stated by Squidward, is a clarinet made out of driftwood that has his name on it. There is also a button on it that, when pushed, shows three wooden Squidwards that play a tune (which is "The Sugar Plum Fairy").
It was given in a blue purple-striped gift box.
Role in series
SpongeBob gives Squidward the wooden clarinet as a Christmas present. SpongeBob is depressed because Santa Claus never came to Bikini Bottom, and he made the clarinet for Squidward so that Squidward wouldn't be left out on Christmas when Santa came, because Squidward didn't believe in Santa. Squidward is touched by SpongeBob's gift and feels bad about how he treated SpongeBob earlier and decides to make up for him by portraying as Santa himself. This leads to Squidward giving away almost everything he owns in his house just to keep SpongeBob's morale up.
Squidward then receives a note from Santa and is shocked to see that he is actually real. Squidward then says that he is insane and goes back inside playing his new wooden clarinet.